# Stag Beetle Elytra: Localized Shape Retention and Puncture/Wear Resistance

^{1}

^{2}

^{3}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Sample Preparation

#### 2.2. Optical and Electron Microscopy

#### 2.3. Mechanical Testing

#### 2.4. Finite Element Simulation

^{3}) were chosen to be in the order of chitin properties [27] as a first approximation. For convenience, the simulations with orthotropic material properties were performed with a constant Poisson’s ratio along the three directions. We used a simplified symmetric model representing one-quarter of the complete geometry and specified two symmetry planes (Figure 3). Identical to the experimental setup, the model was clamped at both the ends and the load (P) was applied in displacement-control mode over a transversal line at the middle of the top surface. The total load was obtained following an incremental approach known as the Riks method [28]. The computational volume was discretized with 9000-s-order tetrahedral elements.

#### 2.5. Nanoindentation

## 3. Results

#### 3.1. Microstructure of the Elytra and the Abdominal Surface

#### 3.2. Deformation of the Elytra

#### 3.3. Puncture and Wear Resistance

^{1.5}/E) [44], which is calculated to be 0.05 ± 0.01 GPa

^{1/2}. These values were close to the values observed in Glycera jaw (~0.077 GPa

^{1/2}) which is known to be wear-resistant [45] and the high abrasion-resistant (0.06–0.08 GPa

^{1/2}) outer layer of the spider fang [44]. Materials with a hard-external layer and relatively softer inner layers enable them to be puncture-resistant and also flexible [46]. Thus, we can see from the above results that the elytra are designed to be both puncture- and wear-resistant. Though our studies are performed on dehydrated samples due to the nature of species selection, we can say that the estimated properties such as wear-resistance and puncture force are of the same order as compared to the hydrated state.

_{g}) and drag force (F

_{d}). It is used to calculate the maximal kinetic energy (E

_{k_max}) that the beetle builds up just before the impact. The kinetic energy values are then compared with the energy absorbed (E

_{a}) by the whole elytra during deflection, using the force (F)-deflection (x) curves. Also, we have performed another calculation to assess the situation of beetles falling with an optimal velocity (v) that is lower than terminal velocity and the corresponding impact energy becomes equal to the amount of energy that can be absorbed by both the elytra, using Equation (7).

_{max}= terminal velocity, ρ = density of the air (1.25 kg/m

^{3}), A = approximated surface area of the beetle (3 cm

^{2}), m = mass of the dehydrated beetle (1.7 g), H

_{max}= maximum height to reach terminal velocity, H = height to reach optimal velocity, and g = acceleration of gravity and ${C}_{d}$ = drag coefficient (1.04, from [47]). The estimated terminal velocity and maximum kinetic energy (E

_{k_max}) of the falling beetle during impact are 9.3 m/s and 72.6 mJ, respectively (Table 2). Also, we estimate the height of fall to reach terminal velocity and the height of optimal velocity to be, 4.4 m and 0.35 m, respectively.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

#### Analytical Estimation of the Snap-Through Curve

_{a}and the rotational stiffness of the hinges A and B is k

_{θ}.

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**Figure 1.**(

**A**) Schematic of a shallow structure in the initial and final configuration. (

**B**) The corresponding response is shown in the load-deflection curve (adapted from [13]).

**Figure 2.**(

**A**) Sample extraction location for the experiments (blue boxes) [25]. (

**B**) Schematic of cross-sectional view of the insect body along the axis of symmetry of the body (white line in A). (

**C**) Clamp set-up used for performing the experiments.

**Figure 3.**Meshed model and coordinate reference system, with highlighted the two symmetry planes (pink) and the applied edge load (P).

**Figure 4.**(

**A**) Primary contact regions of elytra with abdomen. (

**B**) Scanning electron micrograph of the cross-section of an elytron highlighting the different layers [25]. (

**C**) Abdomen surface with folded wings after removal of elytra showing the hinge location (C1), a triangular shaped structure (C2) which accommodates the inner-side corners of elytra, and five surfaces with microtrachia (C4). (

**D**) Magnified image of C2. (

**E**) Scanning electron micrographs of the locking edge surfaces showing the microtrachia.

**Figure 5.**Whole elytra deformation response during loading and unloading. (

**A**) Force-displacement curves and optical image showing the position of applied point force. (

**B**) Elytron shape in the buckled state. (

**C**) Elytron shape recovery after reverse snap-through.

**Figure 6.**Comparison of sectioned elytra force-displacement curves from the experiments, analytical estimation, and the finite element simulation.

**Figure 7.**Force-displacement curves from finite element simulations for different material properties.

**Figure 8.**(

**A**) Schematic showing the experimental set up used for puncture tests. (

**B**) Force curves from the puncture tests, showing the puncture force (highlighted by *). (

**C**) Snapshots from the video during puncturing. (

**D**) (

**i**). Beetle top surface with the punctured hole showing the brittle nature of the top layer; (

**ii**). Brittle nature of the top layer observed from an SEM image of the punctured surface.

**Figure 9.**Images of the mandible. (

**A**) Dark field image of mandible tip, and needle. (

**B**) Front view. (

**C**) Profile view.

**Figure 10.**Optical image of (

**A**) section location (white line). (

**B**) the polished surface with the cuticle cross-section showing the selected locations of the nanoindentation on the external exocuticle, and the (

**C**) force depth curves obtained from the experiments.

Tip Diameter (µm) Measured at 100 µm from the Tip | Average Puncture Force (N) | Puncture Pressure (kPa) | |
---|---|---|---|

Mandible | 338 | 6.9 | 64 |

Needle | 180 | 1.8 | 597 |

**Table 2.**Estimated average values of velocities, heights of fall, kinetic energy of a falling beetle and the energy absorbeded by elytra.

Terminal Velocity (v_{max}) (m/s) | Height to Reach Terminal Velocity, H_{max} (m) | Optimal Velocity (v) | Height to Reach Optimal Velocity, H (m) | Maximum Kinetic Energy (E_{k_max}) (mJ) | Energy Absorbed by Elytra, (2E_{a}) (mJ) |
---|---|---|---|---|---|

9.3 | 4.4 | 1.8 | 0.35 | 72.6 | 5.8 |

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## Share and Cite

**MDPI and ACS Style**

Kundanati, L.; Guarino, R.; Pugno, N.M.
Stag Beetle Elytra: Localized Shape Retention and Puncture/Wear Resistance. *Insects* **2019**, *10*, 438.
https://doi.org/10.3390/insects10120438

**AMA Style**

Kundanati L, Guarino R, Pugno NM.
Stag Beetle Elytra: Localized Shape Retention and Puncture/Wear Resistance. *Insects*. 2019; 10(12):438.
https://doi.org/10.3390/insects10120438

**Chicago/Turabian Style**

Kundanati, Lakshminath, Roberto Guarino, and Nicola M. Pugno.
2019. "Stag Beetle Elytra: Localized Shape Retention and Puncture/Wear Resistance" *Insects* 10, no. 12: 438.
https://doi.org/10.3390/insects10120438